Biodiversity Is Autocatalytic

Ecological Modelling 346 (2017) 70–76

Contents lists available at ScienceDirect

Ecological Modelling

j ournal homepage: www.elsevier.com/locate/ecolmodel

Biodiversity is autocatalytic

a,∗ b c

Roberto Cazzolla Gatti , Wim Hordijk , Stuart Kauffman

Biological Diversity and Ecology Laboratory, Bio-Clim-Land Centre of Excellence, Tomsk State University (TSU), Tomsk, Russia

Konrad Lorenz Institute for Evolution and Cognition Research, Klosterneuburg, Austria

Institute for Systems Biology, Seattle, WA, USA

a r t i c l e i n f o a b s t r a c t

Article history: A central question about biodiversity is how so many species can coexist within the same ecosystem. The

Received 14 October 2016

idea that ecological niches are critical for the maintenance of species diversity has received increasing sup-

Received in revised form 5 December 2016

port recently. However, a niche is often considered as something static, preconditioned, and unchanging.

Accepted 6 December 2016

With the “Biodiversity-related Niches Differentiation Theory” (BNDT), we recently proposed that species

themselves are the architects of biodiversity, by proportionally increasing the number of potentially

Keywords:

available niches in a given ecosystem.

Autocatalytic sets

Along similar lines, but independently, the idea of viewing an ecosystem of interdependent species as

Ecological niches

Biodiversity an emergent autocatalytic set (a self-sustaining network of mutually “catalytic” entities) was suggested,

where one (group of) species enables the existence of (i.e., creates niches for) other species.

Here, we show that biodiversity can indeed be considered a system of autocatalytic sets, and that this

view offers a possible answer to the fundamental question of why so many species can coexist in the

same ecosystem. In particular, we combine the two theories (BNDT and autocatalytic sets), and provide

some simple but formal examples of how this would work.

1. Introduction ecological niche is the role and the position a species has in its

environment (its food and shelter needs, its survival and reproduc-

The variability among living organisms in terrestrial, marine and tion strategies, etc.). The concept of a niche as the set of ecological

other aquatic ecosystems, and the ecological complexes of which requirements, from the reproductive to the alimentary ones, devel-

they are a part, have been deﬁned with the term “biodiversity” (CBD oped by Elton (1927) and improved by Hutchinson (1957) with the

Secretariat, 1992). Apart from the formal deﬁnitions and the dif- deﬁnition of hyper-volume, is a powerful tool for understanding

ferent ways to measure it, the central question about biological the role of each species in its environment.

diversity on Earth is how so many species can coexist within the These multidimensional spaces or hypervolumes that include

same ecosystem (Sherratt and Wilkinson, 2009). all of a species’ interactions with the biotic and abiotic factors of

In an attempt to explain this issue, some authors formalized neu- its environment, led to the consideration of niches as fundamental

tral theories of biodiversity (MacArthur and Wilson, 1967; Hubbell, ecological variables able to regulate species composition and rela-

2001), which assume that all species belonging to the same trophic tions within an ecosystem. For example, it has been suggested that

level of an ecological community are “neutral” in relation to their niche differences stabilize competitor dynamics by giving species

ﬁtness. This implies that there are no real differences between the higher per-capita population growth rates when rare than when

niches of each species and that their success is dictated by the common, and that coexistence occurs when these stabilizing effects

randomness of the moment (Rosindell et al., 2011). of niche differences overcome species in overall competitive ability

In contrast, the idea that niches are critical for the maintenance (Levine and HilleRisLambers, 2009). Moreover, it seems that nest-

of species diversity, challenging the neutral theory of biodiver- edness of niches reduces interspeciﬁc competition and enhances

sity, has received increasing support recently (McGill, 2003). An the number of coexisting species (Bastolla et al., 2009).

Some authors suggested a relationship between the utilization

of ecospace and change in diversity of, for example, marine shelf

faunas through time (Bambach, 1983). However, most of these ∗

Corresponding author.

previous studies emphasized the effect of niche partitioning as a

E-mail addresses: [email protected] (R.C. Gatti),

global long-term pattern in the fossil record to explain the expo-

[email protected] (W. Hordijk), [email protected]

nential diversiﬁcation of life (Benton and Emerson, 2007). The main (S. Kauffman).

http://dx.doi.org/10.1016/j.ecolmodel.2016.12.003

R.C. Gatti et al. / Ecological Modelling 346 (2017) 70–76 71

explanation for a pattern of exponential diversiﬁcation is that as entire set is able to sustain and reproduce itself from a basic food

diversity increases, the world becomes increasingly divided into source. In other words, the set as a whole is self-sustaining and col-

ﬁner niche spaces. This explanation could be a result of the fact that lectively autocatalytic. This concept is intimately related to those

nearly all studies of the impact of species interactions on diversi- of Ulanowicz (2008) and Maturana and Varela (1980), but worked

ﬁcation have concentrated on competition and predation, leaving out in more mathematical detail (Hordijk, 2013).

out the importance of other types of interactions (Joy, 2013). Autocatalytic sets were originally deﬁned in the context of

However, the idea that interactions between species are impor- chemistry (in particular polymer systems; see below), but have

tant catalysts of the evolutionary processes that generate the more recently been extended to study systems in biology (Sousa

remarkable diversity of life is gaining interest among ecologists. For et al., 2015) and possibly economics (Hordijk, 2013). Here, we show

instance, it has been shown that symbiosis between gall-inducing that biodiversity can also be considered a system of autocatalytic

insects and fungi catalyzed both the expansion in resource use sets, and that this view offers a possible answer to the fundamental

(niche expansion) and diversiﬁcation (Joy, 2013). Indeed, facilita- question of why so many species can coexist in the same environ-

tion (a process that allows the colonization and presence of new ment.

species taking advantage of the presence of other ones by expand- In the following sections, we brieﬂy review the Biodiversity-

ing the ecosystem hypervolume) plays a major role in species related Niches Differentiation Theory (BNDT) and the theory of

coexistence, strongly increasing the biodiversity of an area. With autocatalytic sets. The BNDT describes how the number of species in

the “Biodiversity-related Niches Differentiation Theory” (BNDT), an ecosystems changes over time, depending on the number cur-

we recently proposed that species themselves are the architects rently present, and autocatalytic sets can provide a mechanistic

of biodiversity, by proportionally (possibly even exponentially) explanation for this process. This idea is illustrated with a simple

increasing the number of potentially available niches in a given but formal example.

ecosystem (Cazzolla Gatti, 2011).

Fath (2007) suggested that all objects in ecological networks 2. The biodiversity-related niches differentiation theory

interact with and inﬂuence the others in the web and that there are

no null community-level relations. Moreover, network mutualism With the Biodiversity-related Niches Differentiation Theory

is made by community-level relations that usually have a greater (BNDT) (Cazzolla Gatti, 2011), we recently proposed that species

occurrence of mutualism than competition, making them more themselves are the architects of the greatest biodiversity of a given

positive than the direct relations that produced them. Fath (2014) environment, because through the realization of their fundamen-

also proposed that there are no individual species as such, but only tal niche they allow for an expansion of available niches for other

historically contingent constructs that emerge from the structural species. The BNDT states that (Cazzolla Gatti, 2011):

couplings of physical and environmental systems. Species them-

“ . .in natural conditions of immigration and emigration, with

selves, within an ecosystem, appear and disappear over time, as the

every environmental condition, species tend – directly or indi-

environmental conditions allow and construct. A species emerges

rectly, thanks to their simple presence and life roles – to increase

from this environment and is an expression, in fact a historically

the number of potentially available niches for the colonization of

contingent expression, of those interactions. In other words, species

other species, enhancing the limit imposed by the basal hyper-

are expressed and maintained by a complex interacting ecological

volume, until they reach the carrying capacity of the ecosystem.

network.

At the same time, niches and mutualistic networks of the ecosys-

Paraphrasing von Uexküll (1926), the output of one species,

tem allow, through circular and feedback mechanisms, the rise

through a series of direct linkages, indirectly connects back again

of the number of species, generating a non-linear autopoietic

as input to the original “generating” species. In this manner, the

system.”

species affects its own input operating in closed function circles.

Luhmann states that “function systems are operationally closed According to the BNDT, generalist species (e.g. pioneers) expand

and function autopoietically” (quoted in Moeller (2006, p. 101)). the basal ecosystem hypervolume (with a limited number of niches

Autopoiesis is a concept that was introduced by Maturana and available). Once created, the new niches are ﬁlled (through col-

Varela (1980, 1987) to describe a system that uses itself to create onization/immigration) by specialist species. The largest part (in

more of itself, such as a biological cell. terms of time) of the whole process is taken by the “niche expan-

At the ecological scale a similar concept, that of autocatalysis, sion and realization” of the ﬁrst stages. When one or more species

was promoted by Ulanowicz (1995, 2008). Autocatalysis is con- are able to ﬁll the basal niche’s space, and because most species

sidered to be “a necessary condition for maintaining structured are strict for some ecological condition but tolerant for other vari-

gradients that allow for the continuation of system function at ables, the basal ecosystem hypervolume (considered as the sum of

high levels of organization” (Fath, 2014). Ulanowicz (2014) con- every species’ range of variables) enhances its dimensions, allow-

sidered three actors, related in cyclical fashion, each receiving ing other species to colonize the environment. In this way a niche

beneﬁt from its upstream partner and providing beneﬁt to its that was originally forbidden to some species for some ecological

downstream counterpart. Implicit in this conﬁguration resides a characteristics becomes available, simply because of the presence

positive form of selection. The end result is the phenomenon called of another species that can tolerate those initial conditions.

centripetality (Ulanowicz, 1997), whereby internal selection pulls The BNDT was formalized through the differential equation

progressively more resources into the orbit of autocatalysis (usually

dN(t) Ne

at the expense of non-participating elements). = Ne 1 −

dt K

Kauffman (1993) argued that the complexity of biological sys-

tems and organisms might result as much from self-organization where N(t) is the number of niches at time t, Ne is the net number of

and far-from-equilibrium dynamics as from Darwinian natural available niches in the ecosystem, i.e., the difference between the

selection. He also proposed the self-organized emergence of col- number of niches at time t and that at time 0 (Ne = N(t) − N(0)), K

lectively autocatalytic sets of polymers to explain the origin of is the carrying capacity of the ecosystem, and is the coefﬁcient

−

molecular reproduction (Kauffman, 1971, 1986, 1993). An autocat- of niche facilitation, with = St + it et, where St is the number

alytic set is a group of entities (e.g. molecules and the chemical of species at time t, it is the rate of immigration/speciation, and

reactions between them), each of which can be produced catalyt- et the rate of emigration/extinction. Over time, the ecosystem is

ically, i.e., triggered by other entities within the set, such that the subjected to an increase in the number of species proportional to

72 R.C. Gatti et al. / Ecological Modelling 346 (2017) 70–76

the number of species already present in the environment at time

t, with available niches that increase in an exponential way. Sys- 1

tems with a different initial number of species, even if they have

the same physico-chemical basic (abiotic) conditions, will show a r

different number of species after a discrete interval of time t, 3

directly proportional to the number of potential niches developed,

which depends on the initial number of species. Running, instead,

the model towards a longer or inﬁnite time (t → ∞), every ecosys-

tem with identical physico-chemical conditions tends to reach a i i

1 2

similar number of species that is maximum at the succession climax

and at the carrying capacity level (Cazzolla Gatti, 2011).

The BNDT can explain, for instance, why tropical ecosystems are r r

the richest in biodiversity and why ecosystems that receive more 1 2

energy account for more species (i.e., the latitudinal gradient of

biodiversity and the species-energy theory). Based on the predic-

tions of the BNDT, tropical ecosystems, receiving a greater amount

f f f f

of light energy (and thus having higher mean temperatures) and 1 2 3 4

rainfall, possess a larger basal hypervolume than temperate ones

(Cazzolla Gatti, 2016a). Without taking the effects of the BNDT

Fig. 1. An example of a simple RAF set with three reactions {r1, r2, r3}. Black dots

into account, we might mistakenly conclude that the high amount represent molecule types and white boxes represent reactions. Solid (black) arrows

of productivity and available food sources in regions with more are reactants going into and products coming out of a reaction. Dashed (grey) arrows

indicate catalysis. The food set consists of the four molecule types {f1, f2, f3, f4}.

energy does not explain the high biodiversity in these areas. In fact,

there should only be a high quantity of available resources, and not

a greater variety of these, so as to justify the higher abundances and

not the higher richness of species (Sherratt and Wilkinson, 2009). Hordijk and Steel (2004), Hordijk et al. (2011), including an efﬁcient

Instead, the larger basal hypervolume and the biodiversity-related (polynomial-time) algorithm for ﬁnding such sets in any given CRS.

{

niches differentiation could be the reasons why some ecosystems The example RAF set in Fig. 1 requires the food set F = f1, f2, f3,

}

contain more species (Cazzolla Gatti, 2016b). f4 , from which it produces two “intermediate” products i1 and i2,

which are then transformed into a “ﬁnal” product p1. The interme-

diate products i1 and i2 mutually catalyze each other’s production,

3. Autocatalytic sets and RAF theory and the ﬁnal product p1 catalyzes its own production.

Note that this RAF set requires at least two “spontaneous” (i.e.,

Next, we consider the concept of autocatalytic sets, which was uncatalyzed) reaction events before it can be instantiated. At least

ﬁrst introduced and studied by Kauffman (1971, 1986, 1993) in the one of {r1, r2}, and then r3 need to happen spontaneously before

context of the origin of life (Hordijk et al., 2010). It was later formal- all catalysts are present, when starting with only the food set. This

ized mathematically and further developed as RAF theory (Steel, is of course always possible, but at a much lower rate compared

2000; Hordijk and Steel, 2004; Hordijk, 2013). Here, we brieﬂy to when these same reactions are catalyzed. As a consequence,

review the basics of RAF theory and its main results. there may be a (random) “waiting time” before this RAF set is real-

First, we deﬁne a chemical reaction system (CRS) as a tuple ized in a dynamical sense. However, once it is realized, it can in

Q = {X, R, C} R

consisting of a set X of molecule types, a set of chem- principle grow in concentration at an exponential rate, due to its

ical reactions, and a catalysis set C indicating which molecule types (collectively) autocatalytic nature.

catalyze which reactions. We also consider the notion of a food set As argued elsewhere, this requirement for (rare) spontaneous

⊂

F X, which is a subset of molecule types that are assumed to be reactions is actually a useful property for the potential evolvabi-

directly available from the environment (i.e., they do not necessar- lity of autocatalytic sets (Hordijk and Steel, 2014). Furthermore,

ily have to be produced by any of the reactions in the system). it is the main reason why catalysts are treated separately in RAF

The notion of catalysis plays a central role here. A catalyst is a theory, instead of including them in a reaction as both a reactant

molecule that signiﬁcantly speeds up the rate at which a chemical and a product, which is often done in alternative chemical reaction

reaction happens, without being “used up” in that reaction. Cataly- network representations.

sis is ubiquitous in life (van Santen and Neurock, 2006). Almost all RAF theory has been applied extensively to simple polymer-

organic reactions are catalyzed, and catalysts are essential in deter- based models of chemical reaction networks, showing that

mining and regulating the functionality of the chemical networks autocatalytic sets are highly likely to exist in such models, also

that support life. for chemically realistic levels of catalysis (Hordijk and Steel, 2004;

R ⊆ R

An autocatalytic set is now deﬁned as a subset of reac- Mossel and Steel, 2005) and under a wide variety of model assump-

tions (and associated molecule types) which is: tions (Hordijk et al., 2011, 2014a,b; Smith et al., 2014). However,

autocatalytic sets are not just a theoretical construct, as they have

also been created and studied in real chemical networks under con-

1 Reﬂexively Autocatalytic (RA): each reaction r ∈ R is catalyzed

trolled laboratory conditions (Sievers and von Kiedrowski, 1994;

by at least one molecule type involved in R , and

Ashkenasy et al., 2004; Lincoln and Joyce, 2009; Vaidya et al., 2012).

2 Food-generated (F): all molecules involved in R can be created

In fact, the formal RAF framework was used to analyze in detail

from the food set F by using a series of reactions only from R

one of these real autocatalytic networks (Hordijk and Steel, 2013),

itself.

one consisting of 16 catalytic RNA molecules, or ribozymes (Vaidya

et al., 2012). Moreover, it was recently shown using the RAF algo-

A simple example of such a Reﬂexively Autocatalytic and Food- rithm that the metabolic network of Escherichia coli forms a large

generated (RAF) set consisting of three reactions is presented autocatalytic set of close to 1800 reactions (Sousa et al., 2015). As

in Fig. 1, but a RAF set can of course be of any size. A math- far as we know, this is the ﬁrst formal proof that living organisms

ematically more formal deﬁnition of RAF sets was provided in (or at least essential parts thereof) are indeed autocatalytic sets.

R.C. Gatti et al. / Ecological Modelling 346 (2017) 70–76 73

Finally, we have shown that “higher levels” of autocatalytic sets Here, we make these arguments and speculations more concrete

can emerge (Hordijk et al., 2012; Hordijk and Steel, 2015). For by showing a simple but formal example of how this could work.

example, a boundary (such as a lipid layer) can be considered an This then also immediately provides formal support for the BNDT,

additional catalyst: it increases the rate at which reactions hap- as we will discuss below.

pen inside it, by keeping the relevant molecules in close proximity Recall that an autocatalytic (RAF) set depends on a given food set

rather than having them diffuse away, but the boundary itself is not F, i.e., molecules that are directly available from the environment.

used up in those reactions. This way, an “autocatalytic set of auto- However, an autocatalytic set itself produces additional molecules

catalytic sets” emerges, which can form a simple (proto)cell-like which could now also become available to other (potential) auto-

structure (Hordijk and Steel, 2015). This line of reasoning can, of catalytic sets. In other words, each autocatalytic set generates an

course, be extended to then get the next emergent level of autocat- “extended food set” (Hordijk and Steel, 2015). For example, the sim-

alytic sets forming multicellular organisms, and so on, all the way ple RAF set in Fig. 1 generates the ﬁnal product p1 from the food set

up to the species level. F = {f1, f2, f3, f4}, and thus an “extended food set” F = F ∪ {p1}. Conse-

With this RAF formalism and the possibility for higher-level quently, once this RAF set is realized (in a dynamical sense), other

(emergent) autocatalytic sets in place, we now show how RAFs, autocatalytic sets that otherwise would not be realizable (given

niches, and biodiversity can be related to each other. only F) could now potentially also come into existence (using F ).

An example of such a situation is shown in Fig. 2. At the bottom

of this ﬁgure the original example RAF set of Fig. 1 is shown. We

4. RAF sets, niche creation, and autocatalytic biodiversity

have labelled it 1 and enclosed it in a blue dashed ellipse. This

is simply to distinguish it from other reactions that may exist in

In Cazzolla Gatti (2011) we argued that:

the overall reaction network, and does not necessarily represent a

. .

“ species themselves, creating favorable conditions for the physical boundary or membrane. Two other RAF sets (R2 and R3)

colonization of other species, allow their concurrent presence, are also shown, which partially depend on the product p1 generated

. .

[ ] and the fundamental mechanism that supports the coexis- by R1. For example, R2 uses several of the molecules in the original

tence of species is the creation of diversity-related niches.” food set F, but one of its required reactants is p1. Similarly, R3 uses

all the molecules in the original food set F (although in different

Furthermore, in Hordijk et al. (2012) we speculated:

combinations), but needs p1 as one of its catalysts.

. .

“ why not consider any ecology of mutually dependent orga- Strictly speaking, for the original food set F, R2 and R3 are not

nisms as an emergent autocatalytic set, with one (group of) proper RAF sets. Elsewhere, we have called such sets a co-RAF, i.e.,

species enabling the evolution of (i.e., creating niches for) other, a subset of reactions that combined with a proper RAF set forms a

new, species.” larger RAF set (Steel et al., 2013). However, for the extended food

Fig. 2. An example of one RAF set (R1) generating an “extended food set” F = F ∪ {p1}, which allows other RAF sets (R2 and R3) to come into existence as well. R2 needs p1

(produced by R1) as one of its reactants, and R3 needs p1 as one of its catalysts. Neither R2 nor R3 are RAF sets (but are co-RAFs) for the original food set F = {f1, f2, f3, f4}.

However, both are proper RAF sets for the extended food set F .

74 R.C. Gatti et al. / Ecological Modelling 346 (2017) 70–76

set F , as generated by R1, both R2 and R3 are proper RAF sets by dependent autocatalytic sets. First, there is the (faster) time scale

themselves. within one Eco-RAF (species guild). At this time scale, the stability

Taking the “species as higher-level (emergent) autocatalytic and rate of reproduction of components of one particular Eco-RAF

sets” view, as described above, we can now consider a so-called is determined, and phenomena like centripetality play a role. Next,

Eco-RAF as a “guild” of species that exploit the same set of resources there is the (slower) time scale at which new Eco-RAFs come into

in similar but slightly different ways, producing intermediate and existence, depending on which others are already present in the

ﬁnal products/conditions that are able to facilitate other Eco-RAFs ecosystem. This is the time scale at which mutual “enablement”

(i.e., other guilds of species). of RAF sets relates directly to the BNDT, and provides a mechanis-

Thus, an ecological autocatalytic set (Eco-RAF) is a RAF set R, tic explanation for how biodiversity can increase proportionally. Of

where the resources (f) available from the resource (or “food”) course the dynamics at the slower time scale, with new Eco-RAFs

set F are required to allow interactions (“reactions”) r between coming into existence over time, then also reciprocally inﬂuences

species and their own environment (biotic-abiotic reactions). These the dynamics at the faster time scale, within individual Eco-RAFs.

interactions realize (in Hutchinsonian terms) a species’ niche and Finally, additional similarities between RAF sets and ecological

produce intermediate (i) and ﬁnal (p) products/conditions that niches become immediately evident from the Eco-RAF point of view

can catalyze interactions within and among the Eco-RAFs (i.e., the as well. For example, as was mentioned earlier, sometimes there is

guilds), facilitating the realization of other species’ niches and the a (random) waiting time for one or more spontaneous reactions

development of other guilds (R2, R3, etc.) through an extended to happen before a RAF set can be fully realized in a dynamical

resource (“food”) set. sense. The equivalent of this in an ecosystem is the concept of

In an Eco-RAF the primary “reactions” (r) are the biotic-abiotic pioneer species, which are fundamental to start the colonization pro-

interactions, while the secondary reactions are intra-inter-speciﬁc cess and to create the fundamental niche conditions. For example,

interactions, which are included in the Eco-RAFs (guilds) but derive they increase humidity and mineral content of soils, reduce insola-

from the primary ones between each species and its environment. tion, protect against erosion and weathering, etc. And, as was also

Therefore, the intra-inter-speciﬁc interactions are those arising already mentioned, the largest part of the whole colonization pro-

within and among each Eco-RAF set, between the species that cess is taken by this niche expansion and realization phase (the

interact with their own environment and with each other. For “waiting time”), after which new niches are ﬁlled up (and created)

example, r1 (species 1 interacting with environment 1) interacts more quickly.

with r2 (species 2 interacting with environment 2) through the In conclusion, an ecological niche is clearly not only deﬁned by

intermediate (i) and ﬁnal (p) products/conditions they produce the abiotic environment (in this case the original food/resource

(represented by “reaction” r3). These products and conditions can set F), but also by other species guilds (Eco-RAFs) that are

also include non-material elements and behaviours, such as mat- already present in an ecosystem, and which generate an extended

ing calls, warning signals, threat displays, allopatic substances, or food/resources set. Thus, the existence of one or more species

chemical exchanges, which, in turn, can “catalyze” (facilitate) other enables the evolution and/or establishment of other species in

“reactions” (interactions). the same ecosystem. In short, new species create new niches. In

As a simple but realistic example, the autocatalytic set R1 could this way we can say that biodiversity is autocatalytic and that

represent trees, which provide food, as leaves, for monkeys (rep- increasingly diverse ecosystems are its emergent properties. Devel-

resented by autocatalytic set R2) and act as catalysts, by providing opment, whether in nature or in economies, is thus best viewed as

nesting space, for birds (autocatalytic set R3). In such an ecological an open-ended process by which differentiation emerges from gen-

context, R1 can be considered an autotrophic guild of species, and erality, which then become other generalities from which further

R2 and R3 heterotrophic guilds (being partly dependent on R1). differentiation emerges (Jacobs, 2000). Thus, diversity of species

Of course this line of reasoning can easily be extended to higher expands in a rich environment, which is created by the diverse use

trophic levels, as illustrated in Fig. 3, where species guilds (Eco- and reuse of received energy.

RAFs) in each next level depend in various ways on already existing

guilds in lower levels (which provide “reactants” and “catalysts” in

5. Discussion

an extended resource set).

It should be pointed out that there are two different time scales We have argued that biodiversity can be viewed as a system of

involved in this view of ecosystems as a network of mutually autocatalytic sets, and that this view offers a possible answer to

Fig. 3. An ecosystem of several trophic levels of species guilds (Eco-RAFs), where guilds in each next level depend in various ways on products (extended resource sets) of

guilds in previous levels, rather than just the original resource set (the rectangle labelled F).

R.C. Gatti et al. / Ecological Modelling 346 (2017) 70–76 75

the fundamental question of why so many species can coexist in example, the trends of number of genera during the Phanerozoic

the same ecosystem. The idea that species themselves are essential (Rohde and Muller, 2005), which follows an exponential growth

in generating biodiversity, by proportionally (possibly even expo- curve. We argue that, if the answer to the above question is positive,

nentially) increasing the number of potentially available niches this curve should – in absence of catastrophic events – eventually

in a given ecosystem, was already suggested with the BNDT, for reach a plateau and show a sigmoidal curve (as predicted by the

which initial experimental support exists (Cazzolla Gatti, 2011). differential equation of the BNDT).

Here, we have combined this theory with that of autocatalytic sets A more practical and empirically interesting question, which

(RAF theory), which can provide a mechanistic explanation of how could be answered by the “autocatalytic biodiversity hypothesis”,

this process of increasing biodiversity would work, as we have is whether we can estimate the (possible or existing) number of

illustrated with a simple but formal example. species of a particular group from ecological variables (mainly

The concept of autocatalytic sets was originally developed in the inﬂuencing the autocatalysis of that group), such as biomass. For

context of chemistry and the origin of life. The theory has been suc- example, Kauffman (1993) calculated the number of cell types

cessfully applied to study real chemical reaction networks created as the square-root of the number of genes of an organism. Simi-

in the laboratory (Hordijk and Steel, 2013), and also actual living larly, we attempted to calculate the number of vascular plants by

organisms (Sousa et al., 2015). We have even argued that economic taking the square-root of the estimated total live plant biomass

systems could possibly be viewed as autocatalytic sets (Hordijk, of 550 bTC (billion tonnes of carbon) (Groombridge and Jenkins,

2013). If the views expressed here are valid, then the theory can be 2000). The result we obtain is 741,620 vascular plant species. As

extended to the ﬁeld of ecology as well. of 2013, approximately 350,000 are accepted species names and

Ecologists have long questioned how biological diversity is over 240,000 names remain to be resolved into ’accepted name’

maintained. However, after recently being challenged by the neu- or ’synonym’ (see http://www.theplantlist.org/). Considering that

tral theory of biodiversity, which explains coexistence with the an unknown number of plant species have yet to be discovered,

equivalence of competitors, the importance of niches for the and summing the number of accepted species to a mean number

maintenance of species diversity has been restored (Levine and of unresolved names, the ﬁnal sum is surprisingly close to our esti-

HilleRisLambers, 2009). Moreover, many past theories of biodiver- mate. Is this result just a coincidence or is it truly a consequence of

sity that either neglected species interactions (Alonso et al., 2006; the theory? Hopefully we will be able, at some point, to perform a

Volkov et al., 2007) or assumed that species interact randomly with similar calculation for animal groups and resolve this question.

each other (May, 1974; Chesson, 2000), have recently been refuted

by empirical work that revealed that ecological networks are highly Acknowledgements

structured (Bascompte et al., 2003; Montoya et al., 2006; Pascual

and Dunne, 2006).

RCG would like to thank the Bio-Clim-Land Centre of Excellence

Some authors (Bastolla et al., 2009) suggested that the lack

and the Tomsk State University for their support and patience dur-

of a theory that takes into account the structure of interactions

ing the thinking process needed to work on theoretical ecology. WH

precludes further assessment of the implications of such network

thanks the KLI Klosterneuburg for ﬁnancial support through a fel-

patterns for biodiversity, and proposed that the architecture of

lowship. We also thank Brian Fath for valuable feedback, especially

mutualistic networks minimizes competition and increases bio-

regarding relevant literature.

diversity. In this way, the autocatalytic nature of biodiversity (as

proposed here) could represent an explanatory process for the

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